We want to apply for immigration under Quebec Skilled Worker category.
We are from India and are currently based in the USA for last 3 years.
Do we need to get a PCC from both India and USA .or is it ok to just get it from
Either one of them.
Also please let us know if we can submit the application package for the initial
Processing without the PCC .

You need both.
For PCC from India, you can apply at "Indian Consulate" near to your city.
For FBI, get your finger prints done and apply.

For Quebec, you may apply without police certificates showing a proof that you have applied. However, it will not help much to save the time but can delay the things.

The advice is, at least get one certificate ( India or USA) and apply saying that the other one is in process.